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The Leray–Schauder degree theory is used to obtain sufficient conditions for the existence and uniqueness of solutions for the boundary value problem x′′ = f(t, x, x′, x′′, λ), α(x) = 0, β(x) = 0, γ(x) = 0, depending on the parameter λ. Here α, β, γ are linear bounded functionals defined on the Banach space of C0-functions on [0, 1] and x(t) = x(0)− x(t), x(t) = x(1)− x(t).

On a class of functional boundary value problems for the equation x'' = f(t,x,x',x'',λ)